Answer:
−8x+6y−12
Step-by-step explanation:
Distribute:
=(2)(4)+(2)(−2x)+(2)(y)+(−4)(5)+(−4)(x)+(−4)(−y)
=8+−4x+2y+−20+−4x+4y
Combine Like Terms:
=8+−4x+2y+−20+−4x+4y
=(−4x+−4x)+(2y+4y)+(8+−20)
=−8x+6y+−12
Answer:
The 95% confidence interval is ( 27.126 , 34.674)
Step-by-step explanation:
Given
The t critical value at 0.05 level = 2.023 for the df = 39
Confidence interval = 95%
Mean
Substituting the given values we get -
Hence, the 95% confidence interval is
( 27.126 , 34.674)
Answer:
Height of the fighter plane =1.5km=1500 m
Speed of the fighter plane, v=720km/h=200 m/s
Let be the angle with the vertical so that the shell hits the plane. The situation is shown in the given figure.
Muzzle velocity of the gun, u=600 m/s
Time taken by the shell to hit the plane =t
Horizontal distance travelled by the shell =u
x
t
Distance travelled by the plane =vt
The shell hits the plane. Hence, these two distances must be equal.
u
x
t=vt
u Sin θ=v
Sin θ=v/u
=200/600=1/3=0.33
θ=Sin
−1
(0.33)=19.50
In order to avoid being hit by the shell, the pilot must fly the plane at an altitude (H) higher than the maximum height achieved by the shell for any angle of launch.
H
max
=u
2
sin
2
(90−θ)/2g=600
2
/(2×10)=16km
So, the prime factors of 96 are written as 2 x 2 x 2 x 2 x 2 x 3 or 3 x 25, where 2 and 3 are the prime numbers.
